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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2006 • Question 4

Question

Math 6510 • Differentiable Manifolds Fall 2006 • Question 4

Define the Lefschetz index of an isolated fixed point of a smooth map \(f:M\to M\). Compute the Lefschetz index at 0 of the map \(f:\mathbb {C}\to \mathbb {C}\) given by \(f(z)=z+z^m\), \(m>0\).

Raw LaTeX

Define the Lefschetz index of an isolated fixed point of a smooth map
\(f:M\to M\). Compute the Lefschetz index at 0 of the map \(f:\mathbb{C}\to\mathbb{C}\)
given by \(f(z)=z+z^m\), \(m>0\).

Topic Tags

Euler Characteristic and Lefschetz Fixed Point Theorem Fixed Point Theorems and Borsuk-Ulam